x-3=x^2-3x+1

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Solution for x-3=x^2-3x+1 equation:


Simplifying
x + -3 = x2 + -3x + 1

Reorder the terms:
-3 + x = x2 + -3x + 1

Reorder the terms:
-3 + x = 1 + -3x + x2

Solving
-3 + x = 1 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
-3 + -1 + x + 3x + -1x2 = 1 + -3x + x2 + -1 + 3x + -1x2

Combine like terms: -3 + -1 = -4
-4 + x + 3x + -1x2 = 1 + -3x + x2 + -1 + 3x + -1x2

Combine like terms: x + 3x = 4x
-4 + 4x + -1x2 = 1 + -3x + x2 + -1 + 3x + -1x2

Reorder the terms:
-4 + 4x + -1x2 = 1 + -1 + -3x + 3x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-4 + 4x + -1x2 = 0 + -3x + 3x + x2 + -1x2
-4 + 4x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
-4 + 4x + -1x2 = 0 + x2 + -1x2
-4 + 4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-4 + 4x + -1x2 = 0

Factor a trinomial.
(-2 + x)(2 + -1x) = 0

Subproblem 1

Set the factor '(-2 + x)' equal to zero and attempt to solve: Simplifying -2 + x = 0 Solving -2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0 + 2 x = 0 + 2 Combine like terms: 0 + 2 = 2 x = 2 Simplifying x = 2

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {2, 2}

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